PIRSA:18090053 Scientific Series Mathematical physics

DOI10.48660/18090053

Series: Mathematical Physics

Tolmachov, K. (2018). Towards a categorification of a projection from the affine to the finite Hecke algebra in type A. Perimeter Institute. https://pirsa.org/18090053

Tolmachov, Kostiantyn. Towards a categorification of a projection from the affine to the finite Hecke algebra in type A. Perimeter Institute, Sep. 24, 2018, https://pirsa.org/18090053 

@misc{ pirsa_PIRSA:18090053,
  doi = {10.48660/18090053},
  url = {https://pirsa.org/18090053},
  author = {Tolmachov, Kostiantyn},
  keywords = {Mathematical physics},
  language = {en},
  title = {Towards a categorification of a projection from the affine to the finite Hecke algebra in type A},
  publisher = {Perimeter Institute},
  year = {2018},
  month = {sep},
  note = {PIRSA:18090053 see, \url{https://pirsa.org}}
}

Abstract

Work of Bezrukavnikov on local geometric Langlands correspondence and works of Gorsky, Neguţ, Rasmussen and Oblomkov, Rozansky on knot homology and matrix factorizations suggest that there should be a categorical version of a certain natural homomorphism from the affine Hecke algebra to the finite Hecke algebra in type A, sending basis lattice elements on the affine side to Jucys-Murphy elements on the finite side. I will try to explain some of the structures involved and will talk about recent progress towards a construction of such a categorification in the setting of Hecke categories.

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